It is proposed to investigate methods for the design of sequential clinical trials to determine which of two or more treatments is the best, when the observations from the different treatment populations arrive at different rates. In particular, if the allocation of patients to the different treatments is under the control of the experimenter, the allocation rule will be sought that gives reliable conclusions with a minimum number of patients subjected to the inferior treatments. It is proposed to investigate methods for estimating the effect on mortality of eliminating one or more risks from a group of competing risks, as for example deaths from respiratory diseases from all causes of death.